Question

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Phân tích đa thức thành nhân tử: (x - y)^5 + (y - z)^5 + (z - x)^5

HELP ME!!!!!!!!!!

Answer 1

[Đỗ Thảo Nguyên]

(x−y)5+(y−z)5+(z−x)5(x−y)5+(y−z)5+(z−x)5

= x5−5x4y+10x3y2−10x2y3+5xy4−y5+y5−5y4z+10y3z2−10y2z3+5yz4−z5+z5−5z4x+10z3x2−10z2x3+5zx4−x5x5−5x4y+10x3y2−10x2y3+5xy4−y5+y5−5y4z+10y3z2−10y2z3+5yz4−z5+z5−5z4x+10z3x2−10z2x3+5zx4−x5 = −5(x4y−2x3y2+2x2y3−xy4+y4z−2y3z2+2y2z3−yz4+z4x−2z3x2+2z2x3−zx4)

Answer 2

[Athanasia Karrywang]

(x−y)^5+(y−z)^5+(z−x)^5

= x^5−5x^4y+10x^3y^2−10x^2y^3+5xy^4−y^5+y^5−5y^4z+10y^3z^2−10y^2z^3+5yz^4−z^5+z^5−5z^4x+10z^3x^2−10z^2x^3+5zx^4−x^5

= −5(x^4y−2x^3y^2+2x^2y^3−xy^4+y^4z−2y^3z^2+2y^2z^3−yz^4+z^4x−2z^3x^2+2z^2x^3−zx^4)

***bạn tự phân tích nốt phần trong ngoặc đc k****